Integrable Quartic Potentials and Coupled KdV Equations

S. Baker; V. Z. Enolskii; A. P. Fordy

doi:10.1016/0375-9601(95)00267-7

Integrable Quartic Potentials and Coupled KdV Equations

High Energy Physics - Theory 2009-10-28 v1

Authors: S. Baker , V. Z. Enolskii , A. P. Fordy

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the $1:6:1$ integrable case quartic potential. A generalisation of the $1:6:8$ case is similarly related to a different (but gauge related) fourth order Lax operator. We exploit this connection to derive a Lax representation for each of these integrable systems. In this context a canonical transformation is derived through a gauge transformation.

Keywords

kdv equation integrable systems integrable hierarchies

Cite

@article{arxiv.hep-th/9504087,
  title  = {Integrable Quartic Potentials and Coupled KdV Equations},
  author = {S. Baker and V. Z. Enolskii and A. P. Fordy},
  journal= {arXiv preprint arXiv:hep-th/9504087},
  year   = {2009}
}

Comments

LaTex, 11 pages

Integrable Quartic Potentials and Coupled KdV Equations

Abstract

Keywords

Cite

Comments

Related papers